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Applied Drilling Engineering

Chapter 8 Solutions

Adam T. Bourgoyne Jr. Keith K. Millheim Martin E. Chenevert F.S. Young Jr.

Order No. 31656

1.

Eq. 8.19 for rl >

(Fig. 8.9)

X3

o

= e + (90-0) =e - n + t

6

=n -

90°

1:

(r tan(t)

+ 1

1

= [(D

3

- X ) 3

- D )] 1

OB OB

= 4(r 1

o

D

- X ) 3 t = arctan[(O _ D )] 3 1 (r

1

I

I

d'

T~ I

- X )2 + (D - D )2 3 3 1

I-

2 2 2

= (r 1

- X ) 3

+ (D

X 2

= r1

X 2

= r 1 (1 - cos(S» = r 1sin(S)

D2- D 1 D 2

D- D 3 2

= 01 = (0 3 r

1 sin(O) = DB =

3

- D ) 1

Ie I~

- r cos(S) 1

+ r

1

Ie I I

sin(S)

- D ) 1

r

sin(6) 1 ,

I

x~

2

e =ne = (90

1

= -(90

- Q) + (90 - t)

- t) - (90 - 0)

=:~] - ~rccDS [~] I

e = arctan [::

I

I

I

r

r

1

cos(90 - 0) -- --. OB - (D ID

- D

3 0B

3

1

_ 01 )

I

1

= sin(90

- t)

but

D3 - D1 DB

= sin[arctan [D3 r

e = arctan [ D3 .

r 1

1

- D1]

_ X

3

- __ D1] - X

3

- arccos

(D 3 - D1 ) Q~

3 2. Bui1d-and-Ho1d MEAS. DEPTH 2646.00 2746.00 2846.00 2946.00 3046.00 3146.00 3246.00 3346.00 3446.00 3546.00 3646.00 3746.00 3846.00 3946.00 4046.00 4146.00 4246.00 4346.00 4380.00 4480.00 4580.00 4680.00 4780.00 4880.00 4980.00 5080.00 5180.00 5280.00 5380.00 5480.00 5580.00 5680.00 5780.00 5880.00 5980.00 6080.00 6180.00 6280.00 6380.00 6480.00 6580.00 6680.00 6780.00

SURVEY INCL. DIR. 0.00 S17.10W 1.50 S17.10W 3.00 S17.10W 4.50 S17.10W 6.00 S17.10W 7.50 S17.10W 9.00 S17.10W 10.50 S17.l0W 12.00 S17.l0W 13.50 S17.10W 15.00 S17.10W 16.50 S17.10W 18.00 S17.10W 19.50 S17.10W 21.00 S17.l0W 22.50 S17.10W 24.00 S17.10W 25.50 S17.l0W 26.01 S17.l0W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 S17.10W 26.01 -SI7.10W 26.01 S17.10W 26.01 S17.10W

(TVD)

NORTH -SOUTH

EAST -WEST

VERT. SECTION

CLOSURE DIST. OIR.

2646.00 2745.99 2845.91 2945.69 3045.27 3144.57 3243.53 3342.09 3440.16 3537.69 3634.61 3730.86 3826.36 3921.05 4014.86 4107.74 4199.61 4290.42 4321.04 4410.91 4500.79 4590.66 4680.53 4770.40 4860.27 4950.14 5040.01 5129.88 5219.75 5309.62 5399.50 5489.37 5579.24 5669.11 5758.98 5848.85 5938.72 6028.59 6118.46 6208.34 6298.21 6388.08 6477.95

0.00 -1.25 -5.00 -11.25 -20.00 -31.23 -44.95 -61.13 -79.78 "':100.87 -124.40 -150.34 -178.69 -209.41 -242.49 -277.90 -315.63 -355.65 -369.77 -411.68 -453.59 -495.51 -537.42 -579.34 -621.25 -663.17 -705.08 -746.99 -788.91 -830.82 -872.74 -914.65 -956.56 -998.48 -1040.39 -1082.31 -1124.22 -1166.13 -1208.05 -1249.96 -1291.88 -1333.79 -1375.70

0.00 -0.38 -1.54 -3.46 -6.15 -9.61 -13.83 -18.81 -24.54 -31.03 -38.27 -46.25 -54.97 -64.42 -74.60 -85.50 -97.10 -109.41 -113.76 -126.65 -139.55 -152.44 -165.34 -178.23 -191.13 -204.02 -216.91 -229.81 -242.70 -255.60 -268.49 -281.39 -294.28 -307.18 -320.07 -332.97 -345.86 -358.75 -371.65 -384.54 -397.44 -410.33 -423.23

0.00 -1.16 -4 .. 63 -10.41 -18.49 -28.88 -41.56 -56.53 -73.77 -93.27 -115.03 -139.01 -165.22 -193.63 -224.22 -256.96 -291.85 -328.85 -341.90 -380.66 -419.41 -458.17 -496.92 -535.68 -574.44 -613.19 -651.95 -690.70 -729.46 -768.21 -806.97 -845.73 -884.48 -923.24 -961.99 -1000.75 -1039.50 -1078.26 -1117.01 -1155.77 -1194.52 -1233.28 -1272.04

0 N OE 1 S17W 5 S17W 12 S17W 21 S17W 33 S17W 47 S17W 64 S17W 83 S17W 106 S17W 130 S17W 157 S17W 187 S17W 219 SI7W 254 S17W 291 S17W 330 S17W 372 S17W 387 S17W 431 S17W 475 S17W 518 S17W 562 S17W 606 S17W 650 S17W 694 S17W 738 S17W 782 S17W 825 S17W 869 S17W 913 S17W 957 S17W 1001 S17W 1045 S17W 1089 S17W 1132 S17W 1176 S17W 1220 S17W 1264 S17W 1308 S17W 1352 S17W 1395 S17W 1439 S17W

DEPTH

4 MEAS. DEPTH 6880.00 6980.00 7080.00 7180.00 7280.00 7380.00 7480.00 7580.00 7680.00 7780.00 7880.00 7980.00 8080.00 8180.00 8280.00 8380.00 8480.00 8580.00 8680.00 8780.00 8880.00 8980.00 9080.00 9180.00 9280.00 9380.00 9480.00 9580.00 9680.00 9780.00 9880.00 9980.00 10080.00 10180.00 10280.00 10380.00 10480.00 10580.00 10680.00 10780.00 10880.00 10980.00 11080.00 11180.00 11255.00

*

DEPTH (TVD)

NORTH -SOUTH

EAST -WEST

VERT. SECTION

6567.82 6657.69 6747.56 6837.43 6927.30 7017.18 7l07.05 7196.92 7286.79 7376.66 7466.53 7556.40 7646.27 7736.14 7826.02 7915.89 8005.76 8095.63 8185.50 8275.37 8365.24 8455.11 8544.98 8634.86 8724.73 8814.60 8904.47 8994.34 9084.21 9174.08 9263.95 9353.82 9443.70 9533.57 9623.44 9713.31 9803.18 9893.05 9982.92 10072.79 10162.66 10252.54 10342.41 10432.28 10499.68

-1417.62 -1459.53 -1501.45 -1543.36 -1585.27 -1627.19 -1669.10 -1711.02 -1752.93 -1794.84 -1836.76 -1878.67 -1920.59 -1962.50 -2004.42 -2046.33 -2088.24 -2130.16 -2172.07 -2213.99 -2255.90 -2297.81 -2339.73 -2381.64 -2423.56 -2465 .. 47

-436.12 -449.02 -461.91 -474.81 -487.70 -500.59 -513.49 -526.38 -539.28 -552.17 -565.07 -577.96 -590.86 -603.75 -616.65 -629.54 -642.43 -655.33 -668.22 -681.12 -694.01 -706.91 -719.80 -132.70 -745.59 -758 .. 49 -771.38 -784.27 -797.17 -810.06 -822.96 -835.85 -848.75 -861.64 -874.54 ....887.43 -900.32 -913.22 -926.11 -939.01 -951.90 -964.80 -977.69 -990.59 -1000.26

-1310.79 -1349.55 -1388.30 -1427.06 -1465.81 -1504.57 -1543.32 -1582.08

SURVEY INCL. DIR. 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01 26.01

S17.10W S17.10W S17.l0W S17.l0W S17.10W S17.10W S17.10W S17.10W S17.10W S17.l0W S17.l0W S17.l0W S17.l0W S17.l0W S17.l0W S17.l0W S17.10W S17.l0W S17.l0W S17.10W S17.10W S17.10W S17.10W S17.10W S17.10W S17.10W S17.10W S17.10W S17.10W S17.10W S17.l0W S17.l0W S17.l0W S17.10W S17.l0W S17.10W S17.10W S17.l0W S17.l0W S17.10W S17.10W S17.10W S17.10W S17.10W S17.10W

Maximum inclination is 26°.

-2~O7.38

-2549.30 -2591.21 -2633.13 -2675.04 -2716.95 -2758.87 -2800.78 -2842.70 -2884.61 -2926.52 -2968.44 -3010.35 -3052.27 -3094.18 -3136.09 -3178.01 -3219.92 -3251.36

~1620.84

-1659.59 -1698.35 -1737.10 -1775.86 -1814.61 -1853.37 -1892.12 -1930.88 -1969.64 -2008.39 -2047.15 -2085.90 -2124.66 -2163.41 -2202.17 -2240.92 -2279,,68 -2318.43 -2357.19 -2395.95 -2434.70 -2473.46 -2512.21 -2550.97 -2589.72 -2628.48 -2667.23 -2705.99 -2744.75 -2783.50 -2822.26 -2861.01 -2899.77 -2938.52 -2977.28 -3006.34

CLOSURE DIST. DIR. 1483 1527 1571 1615 1659 1702 1746 1790 1834 1878 1922 1966 2009 2053 2097 2141 2185 2229 2273 2316 2360 2404 2448 2492 2536 2580 2623

2667 2711 2755 2799 2843 2886 2930 2974 3018 3062 3106 3150 3193 3237 3281 3325 3369 3402

S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W S17W

5

B) M.D. at end of build is 4,380 ft. M.D. at r.V.D. is 11,255 ft. C and D) Horizontal Departure: End of Build 3,402.00 ft. TVD of 5,450.

Problem No. 2 2000

-- -- -

""-

4000 ,

~

~

~

.

6000

"'" ~,

.c ~

'\

Q. Q)

Q

\

,

"0

\

III

='"'"

CI)

-

8000

l'IS Q)

:E

1

,,

~

i

'\ , '\

10000

Departure - - Inclination

12000

","

""

'.

--!',----------------...; a

500 1000 1500 2000 2500 3000 3500

Departure, ft I

o

i

I

i

f

5

j

20 Inclination, deg 10

6

3.

Eq. 8.20 for rl< X3 (X - r 1 ) 3 tan(t) =---------(D - D1 ) 3

(D - D )

tan(90 - t)

1 3 = ~~---~ (X - r ) 1

3

(D sin(90 - t)

= (D

3

e

- D1 ) 3 (OB)

- D1 )

OB

r

L~l'- ~'

1

= OB

1:'1

cos(90 - Q)

= OB

e = 180 e=

180 - arctan r

where:

L

- (90 - Q) - (90 - t)

[~~~ =:~ :] -

r

1 -DB1 = ~~-~ (D - ° ) .

3

1

arccos

1)

3

1

[~i]· ~X~ -J

-:....

rl

~

X 3

[(

0

- 0.. 1 ']

. • Sin[arctanex: - r1'

0 3 - 0 1] - arctan [ 1:'1 _ X - accos

~:8-

I

0

OB

therefore:

e = 180

I

(D 3 - D1 )

[ r]

= (03•. 1..0

-

I~

I

D3

t

-

IQ I

C',

l*.

Then from point 0: 180 = e + (90 - Q) + (90 - t) o e- 0 - t

e = =Q +

o

1/

J

7 4. Build-and-Hold MEAS. DEPTH 2013.00 2113.00 2213.00 2313.00 2413.00 2513.00 2613.00 2713.00 2813.00 2913.00 3013.00 3113.00 3213.00 3313.00 3413.00 3513.00 3613.00 3713.00 3813.00 3913.00 4013.00 4113.00 4213.00 4313.00 4413.00 4463.00 4563.00 4663.00 4763.00 4863.00 4963.00 5063.00 5163.00 5263.00 5363.00 5463.00 5563.00 5663.00 5763.00 5863.00 5963.00 6063.00

SURVEY DIR. INCL. 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 22.00 24.00 26.00 28.00 30.00 32.00 34.00 36.00 38.00 40.00 42.00 44.00 46.00 48.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00

N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E

DEPTH (TVD)

NORTH -SOUTH

EAST -WEST

VERT. SECTION

2013.00 2112.98 2212.84 2312.45 2411.70 2510.46 2608.62 2706.05 2802.64 2898.27 2992.81 3086.17 3178.21 3268.84 3357.93 3445.39 3531.10 3614.97 3696.88 3776.74 3854.45 3929.92 4003.05 4073.75 4141.95 4175.08 4240.68 4306.29 4371.89 4437.50 4503.11 4568.71 4634.32 4699.92 4765.53 4831.13 4896.74 4962.34 5027.95 5093.55 5159.16 5224.77

0.00 0.00 1.23 4.93 11.10 19.71 30.77 44.27 60.17 . 78.47 99.15 122.16 147.50 175.13 205.01 237.11 271.39 307.81 346.32 386.87 429.43 473.92 520.31 568.53 618.53 670.24 696.72 750.09 803.45 856.82 910.18 963.55 1016.92 1070.28 1123.65 1177.01 1230.38 1283.74 1337.11 1390.48 1443.84 1497.21 1550.57

0.00 0.00 1.23 4.93 11.10 19.71 30.77 44.27 60.17 78.47 99.15 122.17 147.50 175.13 205.01 237.11 271.39 307.81 346.32 386.88 429.43 473.93 520.31 568.53 618.53 670.24 696.72 750.09 803.45 856.82 910.19 963.55 1016.92 1070.28 1123.65 1177.02 1230.38 1283.·75 1337.11 1390.48 1443.85 1497.21 1550.58

0.001.75 6.98 15.69 27.88 43.52 62.60 85.10 110.98 140.21 172.77 208.60 247.67 289.93 335.33 383.81 435.31 489.77 547.12 607.30 670.23 735.83 804.03 874.74 947.87 985.31 1060.78 1136.26 1211.73 1287.20 1362.67 1438.14 1513.61 1589.08 1664.55 1740.02 1815.49 1890.96 1966.43 2041.90 2117.37 2192.85

CLOSURE DIST. DIR.

--

0 2 7 16 28 44 63 85 III

140 173 209 248 290 335 384 435 490 547 607 670 736 804 875 948 985 1061 1136 1212 1287 1363 1438 1514 1589 1665 1740 1815 1891 1966 2042 2117 2193

N OE N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E

8 MEAS. DEPTH 6163.00 6263.00 6363.00 6463.00 6563.00 6663.00 6763.00 6863.00 6963.00 7063.00 7163.00 7263.00 7363.00 7463.00 7563.00 7663.00 7763.00 7863.00 7963.00 8063.00 8163.00 8263.00 8363.00 8463.00 8563.00 8663.00 8763.00 8863.00 8963.00 9063.00 9163.00 9263.00 9363.00 9463.00 9563.00 9663 .. 00 9763.00 9863.00 9963.00 10063.00 10163.00 10263.00 10363.00 10445.00

SURVEY DIR. INCL. 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.0Q 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49 .. 00 49.00 49.00 49.00 49.00 49.00 49.00 49.00 49.00

N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45 ..00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N4S .. 00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E N45.00E

DEPTH (TVD)

NORTH -SOUTH

EAST -WEST

VERT. SECTION

CLOSURE DIST. DIR.

5290.37 5355.98 5421.58 5487.19 5552.79 5618.40 5684.00 5749.61 5815.21 5880.82 5946.43 6012.03 6077.64 6143.24 6208.85 6274.45 6340.06 6405.66 6471.27 6536.87 6602.48 6668.09 6733.69 6799.30 6864.90 6930.51 6996.11 7061..72 7127.32 7192.93 7258.54 7324.14 7389. 75 7455.35 7520.96 7586,,56 7652.17 7717.77 7783.38 7848.98 7914.59 7980.20 8045.80 8099.60

1603.94 1657.30 1710.67 1764.04 1817.40 1870.77 1924.13 1977.50 2030.86 2084.23 2137.60 2190.96 2244.33 2297.69 2351.06 2404.43 2457.79 2511.16 2564.52 2617.89 2671.25 2724.62 2777.99 2831.35 2884.72 2938.08 2991.45 3044.81 3098.18 3151.55 3204.91 3258.28 3311.64 3365.01 3418.37 3471.74 3525.11 3578.47 3631.84 3685.20 3738.57 3791.93 3845.30 3889.06

1603.94 1657.31 1710.68 1764.04 1817.41 1870.7.7 1924.14 1977.51 2030.87 2084.24 2137.60 2190.97 2244.34 2297.70 2351.07 2404.43 2457.80 2511.17 2564.53 2617.90 2671.26 2724.63 2778.00 2831.36 2884.73 2938.09 2991.46 3044.83 3098.19 3151.56 3204.92 3258.29 3311.66 3365.02 3418.39 3471.75 3525.12 3578.49 3631.85 3685.22 3738.58 3791.95 3845.31 3889.07

2268.32 2343.79 2419.26 2494.73 2570.20 2645.67 2721.14 2796.61 2872.08 2947.55 3023.02 3098.49 3173.96 3249.43 3324.91 3400.38 3475.85 3551.32 3626.79 3702.26 3777.73 3853.20 3928.67 4004.14 4079.61 4155.08 4230.55 4306.02 4381.49 4456.96 4532.43 4607.91 4683.37 4758.85 4834.32 4909.79 4985.26 5060.73 5136.20 5211.67 5287.14 5362.61 5438.08 5499.97

2268 2344 2419 2495 2570 2646 2721 2797 2872 2948 3023 3098 3174 3249 3325 3400 3476 3551 3627 3702 3778 3853 3929 4004 4080 4155 4231 4306 4381 4457 4532 4608 4683 4759 4834 4910 4985 5061 5136 5212 5287 5363 5438 5500

Maximum inclination is 49°. B) M"D. at end of build is 4,463 ft.

A)

--

N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E N45E

9

M.D. at T.V.D. is 10,455 ft. C and D)

Horizontal Departure: End of Build 5,500.00 TVD of 3,100 214.00 TVD of 5,100 2,049.37 TVD of 7,100 4,349.77

Measured Depth: ft. ft. ft. ft.

3,128.03 ft. 5,872.83 ft. 8,921.35 ft.

Problem No. 4 2000 ~--------------

4000

~

..

6000

.c ~

Q.

QJ Q

8000

10000

12000

J I __

Departure

Inclination

..-

1_~_~ o

1000

2000

-.:

3000

4000

5000

Departure, ft i i.

o

i

5

10

)

i

I

"

j

15 20 2G 30 3S 40 4G GO

Inclination, deg

10

5.

From triangle AOO'

e = (90

- B) - (90 - 0)

= 90

- 0

Then from triangle OHO' (90 - 0) can be written as: (r

90 - 0 = arccos

+ r )

1 2 00'

02

but (r

1

+ r )

2

00'

=

[] D ) 1

. [